When comparing Telegram vs Matrix, the Slant community recommends Telegram for most people. In the question“What is the best chat software?”Telegram is ranked 1st while Matrix is ranked 2nd. The most important reason people chose Telegram is:

Copy/paste videos, gifs, images, geolocation, and documents, drag over files for practically any time up to 1.5GB in size. Images can be compressed, too.

Pros

Pro

Free and convenient large file sharing

Copy/paste videos, gifs, images, geolocation, and documents, drag over files for practically any time up to 1.5GB in size. Images can be compressed, too.

Pro

Privacy focused

In addition to the end-to-end encryption that provides privacy to communications, the app also includes self destructing timers for chats, and the ability to permanently delete messages, yours and theirs, from your device.

Pro

Secure

Telegram uses an open source MTProto encryption protocol that provides complete end-to-end encryption for secret chats. To show off their confidence in the protocol the company behind Telegram has organized $200,000 and $300,000 challenges to break the encryption. So far there have been no winners.

Pro

Beautiful UI

Very customizable with a lot of clean looking options.

Pro

Media messaging

Videos, gifs, images, geolocation, and documents.

Pro

Possible to send photos and videos without compression

Pro

2-step verification

You can set up an additional password to your account, which can be reset by your email. You don't have to use an email if you do not want to. If you lose access to your email or forget your password, you will be able to reset it via text message if your account is over seven days old and will receive it within a week (in case you recover anything before then).

Pro

Channels for one way broadcasting

Broadcasting channels suitable for announcing things.

Pro

Free of cost

The application is available free of cost.

Pro

Customer support is within the app

Although it's volunteer based, but still pretty top-notch if available, which it tends to be.

Pro

Supergroups of up to 5000 people

In Supergroups, anyone along with admins can delete their messages from all sides. A message can be pinned to the top. All of the user's messages can be deleted by an administrator, and they can be banned and reported as well. Supergroups can have a public link (outside of Asia, due to high spam volumes), which is also a username.

Pro

Desktop app handles HIDPI

The desktop app has a built in setting to scale the UI of the app up to 200% which allows for those with 4k monitors/screens to use the app without scaling issues.

Pro

Save time with inline bots and link previews

Unfortunately, on the desktop videos don't play, but images are viewable without visiting popular websites like imgur and Instagram.

You can play YouTube videos and others within the app, so you don't need to embed code or anything.

With inline bots, such as @gif, @pic/bing, @vid/YouTube, etc, you can look things up without leaving the client or chat that you're in. Simply type the name and some keywords and wait for the results to load.

Pro

Cloud chat keys are kept in different jurisdiction

Even though encryption used for cloud-based storage (e.g. Gmail, Facebook, iCloud) may not be as secure as end-to-end encryption or zero-knowledge storage, Telegram does the most that it can by holding keys to chats in different jurisdictions, requiring intergovernmental cooperation to obtain the keys. This is aside from whatever other security measures have been taken, of course.

Pro

High quality calls

Uses the latest GPL audio codecs, such as Opus, an adaptative high-quality codec that supersedes AAC at any bitrate.

Pro

Has an easy to use client called Riot

Riot.im is the easiest way to use Matrix, with great clients for Web, iOS and Android (and Fdroid).

Pro

Bridges other networks into a single decentralised network

Matrix has bridges to IRC (freenode, moznet, oftc, snoonet etc), Slack, Gitter, Rocket.Chat, XMPP, SMS, SIP and others. The point is to 'matrix' all the different networks out there into one single decentralised network.

Pro

Built on an open standard

Matrix is an open standard, defining simple HTTP APIs so that devs can easily write their own clients, bots, bridges or servers. You're not locked into a specific set of implementations.

Pro

Does not require a centralized server to establish a connection between two users

Matrix is decentralized, there's no one central point that the information goes through and so no once central point of failure or control.

Pro

Supports different kinds of communication

Matrix is designed to support Instant Messaging, VoIP/WebRTC signalling (voice and video) and Internet of Things communication.

Pro

Has an app store for 3rd party integrations & bots

Riot.im includes an app store with integrations for Github, JIRA, Jenkins, Giphy etc - and anyone can add more via Matrix.

Pro

Offers choice of clients

Pro

Has an active community behind it

Pro

Maintains full conversation history

Pro

Can be integrated with existing communication services

Matrix is designed to support Instant Messaging, VoIP/WebRTC signalling and Internet of Things communication and allows cross-communication between those services. Meaning one person could be using IRC and another Slack for IMs, or one person could be using Skype and another Google Hangouts for videoconferencing.

Pro

Matrix prioritizes direct messaging with people the same as Slack-style groups

Matrix aims to "provide an analogous ecosystem to email - one where you can communicate with pretty much anyone, without caring what app or server they are using" using a neutral identity system.

Pro

End-to-end encryption

Matrix features end-to-end encrypted chats which are syncronized accross all your devices.

Cons

Con

Not fully open source

Telegram has an open API and protocol free for everyone, but the backend software is not open source. Therefore 100% privacy can not be evaluated.

Con

Only "Secret Chat" messages are encrypted end to end

The only way to get end-to-end encryption (client-client) using Telegram is to use the Secret Chat function, anything through the service is server-client encrypted. Also secret chat is only implemented in the mobile apps, meaning there is no way to encrypt messages end-to-end when using the desktop client or the web browser client.

Con

Can only be used with a phone number.

It is not possible to activate and use Telegram by mail etc. You need a phone number.

Con

Can only "redact" a posted message but neither "delete" nor "edit" it.

The ability to edit a posted message is a powerful feature that has come to be expected since the rise of social media. Several other major chat platforms include this feature. Matrix.org's protocols enable you to "redact" a message (mark it as redacted whereas it is removed from view), but not truly delete or edit it. Deletion and editing are in the works, but in the meantime... CON.

Con

Keys cannot be checked automatically

You cannot automatically check keys of your recepients. Only manually.